Making Splice Repairs are not as hard as you would think. I have seen people replace some very nice stock just because it was missing a chip of wood.
This post will walk you through a repair .

As always, we need a Victim. For this post I will use a M1 Carbine.
This type of damage is very common on Carbine stocks. Most of the time it is caused by the improper fitting of the recoil plate.

First you will need to mill out the damaged area. This can be done with a Dremel tool and a highspeed cutting bit or wood files. You will need to square up the damaged area so that a new piece of wood can be fitted.

Then cut a pice of wood to fit the area. Try to match the wood as close as possible, this will help to blend the repair. Try and cut your replacement piece so that it fits sung and test fit it.

I like to use Brownell's Acraglass for my repairs, but a clear epoxy like Devcon 2 Ton Epoxy with the 30 min. set time can be used. Do not use super glue, wood glues or any of the 5 min. epoxys, they will not hold up in the long run.
Once you have applied the resin, clamp the piece in place.

Once the resin has cured, trim the pice of wood down close to where you need it with a dremel tool or file.

Then dress it up using a sanding block and sand paper.

The hardest part of a repair can be blending in the finish. Most offten I use alcohol base stains or dye to blend the finish.